How can one keep a \section from being at the end of a page?

You should use the option

\usepackage[nobottomtitles*]{titlesec}

This will prevent your heading titles to be displayed at the bottom of the page and it will place your heading in the next page.

As Will Robertson says, this really should not be happening with standard document classes and packages. You might like to try redefining the sectioning commands with the titlesec package; I usually do this anyway to get the section heading styles I want, and titlesec has features to control the breaking and positioning of section headings.

The other suggestions regarding \widowpenalty and enlarging the page are not helpful here; they're for problems with regular flowing text, and section headings mess up the normal flow with their spacing commands.

Edit: What's probably happening is that you have a chapter with non-text material that's forcing TeX to choose the "least bad" break it can, which in this case happens to be splitting a section heading from its contents; this is Really Bad, but if it's the only option it's the only option. Usually this is caused by floats; if you have floats near the problem heading, you may try playing with them. Or not playing with them; LaTeX floats are dread beasts only the bravest dare do true battle with.

For a quick fix, you can try the titlesec package as I mentioned earlier. The titlesec manual gives (section 9.2, page 26 of 27) titlesec versions of the standard LaTeX headings. The LaTeX sectioning commands are well known to be ugly, internally and externally (the non-chapter headings aren't so bad, but the rumor that the standard classes were designed to be so ugly that people would be obligated to create their own classes exists for a reason). Paste the following into your preamble (before \begin{document}) and see if it helps after rerunning LaTeX until it stabilizes:

\usepackage{titlesec}
\titleformat{\chapter}[display]
{\normalfont\huge\bfseries}{\chaptertitlename\ \thechapter}{20pt}{\Huge}
\titleformat{\section}
{\normalfont\Large\bfseries}{\thesection}{1em}{}
\titleformat{\subsection}
{\normalfont\large\bfseries}{\thesubsection}{1em}{}
\titleformat{\subsubsection}
{\normalfont\normalsize\bfseries}{\thesubsubsection}{1em}{}
\titleformat{\paragraph}[runin]
{\normalfont\normalsize\bfseries}{\theparagraph}{1em}{}
\titleformat{\subparagraph}[runin]
{\normalfont\normalsize\bfseries}{\thesubparagraph}{1em}{}
\titlespacing*{\chapter} {0pt}{50pt}{40pt}
\titlespacing*{\section} {0pt}{3.5ex plus 1ex minus .2ex}{2.3ex plus .2ex}
\titlespacing*{\subsection} {0pt}{3.25ex plus 1ex minus .2ex}{1.5ex plus .2ex}
\titlespacing*{\subsubsection}{0pt}{3.25ex plus 1ex minus .2ex}{1.5ex plus .2ex}
\titlespacing*{\paragraph} {0pt}{3.25ex plus 1ex minus .2ex}{1em}
\titlespacing*{\subparagraph} {\parindent}{3.25ex plus 1ex minus .2ex}{1em}

With those definitions in place, your section headings should look just about identical, but internally be generated by titlesec's cleaner code, and hopefully exhibit saner behavior. Without seeing the document in question it's hard to predict if they'll help or not, but the fix is easy enough that it's worth a shot. Also, this exposes the commands' definitions for tweaking -- if you adjust the spacing values for \section in that block I'm sure you'll be able to find something that works (but it might be even uglier than the broken header!). You can also get ambitious and try defining your own heading styles, but this is 1) a waste of time for documents shorter than book length and 2) likely to go horribly wrong without some experience in typography and/or design.

Hope that helps.

This should rarely happen with the standard document classes (and the better-known ones such as memoir and koma). Are you using a homegrown document class or redefining the \section command yourself?